Characteristic value determination from small samples

The paper deals with the characteristic value determination from relatively small samples. When the distribution and its parameters of a random variable are known, the characteristic value is deterministic quantity. However, in practical problems the parameters of distribution are unknown and can only be estimated from random samples. Therefore the characteristic value is by itself a random variable. The estimates of characteristic values are strongly dependant on the distribution of random variable. In the paper we show the analytical solution for characteristic value determination from random samples of normal and lognormal random variables. The confirmation of analytical results is accomplished by the use of computer simulations. For Gumbel, and Weibull distribution the characteristic value estimates are obtained numerically by combination of simulations and bisection method. In the paper the numerical results are presented for 5% characteristic values with 75% confidence interval, which is in accord with the majority of European building standards. The proposed approach is demonstrated on the data of experimentally obtained bending strengths of finger jointed wooden beams. (C) 2006 Elsevier Ltd. All rights reserved

Flux vortex dynamics in type-II superconductors

Abstract The flux-pinning landscape in type-II superconductors determines the response of the flux line lattice to changing magnetic fields. Typically, the flux vortex behaviour is hysteretic and well described within the framework of the Bean critical-state model and its extensions. However, if the changing magnetic field does not move the flux vortices from their pinning sites, their response remains linear and reversible. The vortex displacement, then, is characterised by the Campbell penetration depth, which itself is related directly to the effective size of the pinning potential. Here, we present measurements of the Campbell penetration depth (and the effective size of the pinning potential) as a function of magnetic field in a single-grain bulk GdBa2Cu3O 7 − δ superconductor using a pick-up coil method. Hence, the hysteretic losses, which take into account the reversible vortex movement, are established.This work was supported by Siemens AG. Dr Mark Ainslie would like to acknowledge financial support from an Engineering and Physical Sciences Research Council (EPSRC) Early Career Fellowship EP/P020313/1

Composite stacks for reliable > 17 T trapped fields in bulk superconductor magnets

Trapped fields of over 20 T are, in principle, achievable in bulk, single-grain high temperature cuprate superconductors. The principle barriers to realizing such performance are, firstly, the large tensile stresses that develop during the magnetization of such trapped-field magnets as a result of the Lorentz force, which lead to brittle fracture of these ceramic-like materials at high fields and, secondly, catastrophic thermal instabilities as a result of flux movement during magnetization. Moreover, for a batch of samples nominally fabricated identically, the statistical nature of the failure mechanism means the best performance (i.e. trapped fields of over 17 T) cannot be attained reliably. The magnetization process, particularly to higher fields, also often damages the samples such that they cannot repeatedly trap high fields following subsequent magnetization. In this study, we report the sequential trapping of magnetic fields of ~ 17 T, achieving 16.8 T at 26 K initially and 17.6 T at 22.5 K subsequently, in a stack of two Ag-doped GdBa2Cu3O7-{\delta} bulk superconductor composites of diameter 24 mm reinforced with (1) stainless-steel laminations, and (2) shrink-fit stainless steel rings. A trapped field of 17.6 T is, in fact, comparable with the highest trapped fields reported to date for bulk superconducting magnets of any mechanical and chemical composition, and this was achieved using the first composite stack to be fabricated by this technique

Penetration depth of shielding currents due to crossed magnetic fields in bulk (RE)-Ba-Cu-O superconductors

Exposure to time-varying magnetic fields causes shielding currents to flow beneath the surface of a superconductor up to a field-dependent penetration depth. In trapped-field applications of bulk superconductors, in which the decay of trapped field due to external AC magnetic fields is caused by current redistribution (and not by heating and temperature rise), this penetration depth determines the degree of current redistribution in the superconductor and, in turn, the degree of decay of trapped field. In this study we propose and validate experimentally a model to explain the rate of decay of trapped field in a single grain bulk GdBa2Cu3O7- (GdBCO) superconductor exposed to an AC magnetic field in a crossed-field configuration. The model is based on calculating the time dependence of the trapped field using the Biot-Savart law and assuming that the time dependence of the current density changes at the depth of penetration of the induced shielding currents. Inside the superconductor, where the crossed-field has not penetrated, the time dependence is assumed to be logarithmic and the decay of current density due to flux creep, whereas within the penetration depth of the surface the time dependence is assumed to be exponential and the decay of current density due to its redistribution. The penetration depth was measured separately using SQUID magnetometry and used as an input parameter to the model. The model was compared subsequently with measurements of the decay of trapped field and found to be in excellent agreement with the observed behaviour.Siemens AG EPSRC EP/P00962X/

Exploiting flux jumps for pulsed field magnetisation

Magnetisation is one of the main barriers to practical use of bulk superconductors as high field magnets. Recently several authors have reported a flux jump effect that allows penetration of magnetic flux into a bulk superconductor during pulsed field magnetisation (PFM) at lower fields than that would be predicted on the basis of the Bean model. We have systematically investigated macroscopic flux jumps in single grain GdBa2Cu3O7-δ-Ag (GdBCO-Ag) bulk superconductors with diameters of up to 30 mm when subjected to pulsed magnetic fields. Flux jumps were observed at temperatures between 30 K and 77 K and in applied magnetic fields of up to 7 T. The applied pulsed field required to trigger the instability or flux jump field, Bj, was determined experimentally and found to increase with decreasing temperature. An extended instability criterion based on a 2D axisymmetric model was used to predict Bj at various temperatures and the results are in good agreement with experiments. A significant temperature rise has been measured experimentally during the magnetisation process which indicates that local heat generation due to the sharp rise of the applied field in the PFM process is the primary cause of the flux jumps. The experimental results suggest further that the critical current density reduces to almost zero in the warm part of the sample during the short period of non-equilibrium. A peak trapped field of 4.1 T at the surface and 5.3 T between a stack of two GdBCO-Ag bulk superconductors was achieved at 30 K by means of an optimized two- step pulse sequence with the assistance of the flux jumps, which is extremely promising for potential applications of these technologically important materials.This work was supported by the Siemens Company and by the Engineering and Physical Sciences Research Council (grant number: EP/P00962X/1). Mark Ainslie would like to acknowledge financial support from an Engineering and Physical Sciences Research Council (EPSRC) Early Career Fellowship EP/P020313/1

Penetration depth of shielding currents due to crossed magnetic fields in bulk (RE)-Ba-Cu-O superconductors

© 2019 IOP Publishing Ltd. Exposure to time-varying magnetic fields causes shielding currents to flow beneath the surface of a superconductor up to a field-dependent penetration depth. In trapped field applications of bulk superconductors, in which the decay of trapped field due to external AC magnetic fields is caused by current redistribution (and not by helating and temperature rise), this penetration depth determines the degree of current redistribution in the superconductor and, in turn, the degree of decay of trapped field. In this study we propose and validate experimentally a model to explain the rate of decay of trapped field in a single grain bulk GdBa 2 Cu 3 O 7-δ (GdBCO) superconductor exposed to an AC magnetic field in a crossed-field configuration. The model is based on calculating the time dependence of the trapped field using the Biot-Savart law and assuming that the time dependence of the current density changes at the depth of penetration of the induced shielding currents. Inside the superconductor, where the crossed-field has not penetrated, the time dependence is assumed to be logarithmic and the decay of current density due to flux creep, whereas within the penetration depth of the surface the time dependence is assumed to be exponential and the decay of current density due to its redistribution. The penetration depth was measured separately using SQUID magnetometry and used as an input parameter to the model. The model was compared subsequently with measurements of the decay of trapped field and found to be in excellent agreement with the observed behaviour

Exploiting flux jumps for pulsed field magnetisation

Magnetisation is one of the main barriers to practical use of bulk superconductors as high field magnets. Recently several authors have reported a flux jump effect that allows penetration of magnetic flux into a bulk superconductor during pulsed field magnetisation (PFM) at lower fields than that would be predicted on the basis of the Bean model. We have systematically investigated macroscopic flux jumps in single grain GdBa2Cu3O7-δ-Ag (GdBCO-Ag) bulk superconductors with diameters of up to 30 mm when subjected to pulsed magnetic fields. Flux jumps were observed at temperatures between 30 and 77 K and in applied magnetic fields of up to 7 T. The applied pulsed field required to trigger the instability or flux jump field, B j, was determined experimentally and found to increase with decreasing temperature. An extended instability criterion based on a 2D axisymmetric model was used to predict B j at various temperatures and the results are in good agreement with experiments. A significant temperature rise has been measured experimentally during the magnetisation process which indicates that local heat generation due to the sharp rise of the applied field in the PFM process is the primary cause of the flux jumps. The experimental results suggest further that the critical current density reduces to almost zero in the warm part of the sample during the short period of non-equilibrium. A peak trapped field of 4.1 T at the surface and 5.3 T between a stack of two GdBCO-Ag bulk superconductors was achieved at 30 K by means of an optimised two-step pulse sequence with the assistance of the flux jumps, which is extremely promising for potential applications of these technologically important materials

Flux vortex dynamics in type-II superconductors

The flux-pinning landscape in type-II superconductors determines the response of the flux line lattice to changing magnetic fields. Typically, the flux vortex behaviour is hysteretic and well described within the framework of the Bean critical-state model and its extensions. However, if the changing magnetic field does not move the flux vortices from their pinning sites, their response remains linear and reversible. The vortex displacement, then, is characterised by the Campbell penetration depth, which itself is related directly to the effective size of the pinning potential. Here, we present measurements of the Campbell penetration depth (and the effective size of the pinning potential) as a function of magnetic field in a single-grain bulk GdBa2Cu3 ALIGN="MIDDLE" ALT="$$" SRC="sustab5b53ieqn1.gif" superconductor using a pick-up coil method. Hence, the hysteretic losses, which take into account the reversible vortex movement, are established

Composite stacks for reliable > 17 T trapped fields in bulk superconductor magnets

Trapped fields of over 20 T are, in principle, achievable in bulk, single-grain high temperature cuprate superconductors. The principle barriers to realizing such performance are, firstly, the large tensile stresses that develop during the magnetization of such trapped-field magnets as a result of the Lorentz force, which lead to brittle fracture of these ceramic-like materials at high fields and, secondly, catastrophic thermal instabilities as a result of flux movement during magnetization. Moreover, for a batch of samples nominally fabricated identically, the statistical nature of the failure mechanism means the best performance (i.e. trapped fields of over 17 T) cannot be attained reliably. The magnetization process, particularly to higher fields, also often damages the samples such that they cannot repeatedly trap high fields following subsequent magnetization. In this study, we report the sequential trapping of magnetic fields of ~ 17 T, achieving 16.8 T at 26 K initially and 17.6 T at 22.5 K subsequently, in a stack of two Ag-doped GdBa2Cu3O7-{\delta} bulk superconductor composites of diameter 24 mm reinforced with (1) stainless-steel laminations, and (2) shrink-fit stainless steel rings. A trapped field of 17.6 T is, in fact, comparable with the highest trapped fields reported to date for bulk superconducting magnets of any mechanical and chemical composition, and this was achieved using the first composite stack to be fabricated by this technique